A large static magnetic field is used by Magnetic Resonance Imaging (MRI) scanners to align the nuclear spins of atoms as part of the procedure for producing images within the body of a patient. This large static magnetic field is referred to as the B0 field or the main magnetic field.
One method of spatially encoding is to use magnetic field gradient coils. Typically there are three coils which are used to generate three different gradient magnetic fields in three different orthogonal directions.
During an MRI scan, Radio Frequency (RF) pulses generated by one or more transmitter coils cause a called B1 field. Additionally applied gradient fields and the B1 field do cause perturbations to the effective local magnetic field. RF signals are then emitted by the nuclear spins and detected by one or more receiver coils. These RF signals contain image data encoded in k-space. The central region of k-space generally contains more image information than outer regions of k-space. The Nyquist sampling theorem is a sufficient, but not necessary condition. Often times an acceptable magnetic resonance image can be reconstructed by sampling k-space less than is specified by the Nyquist theorem.
The review article Lustig, Michael, et al. “Compressed sensing MRI.” IEEE Signal Processing Magazine 25.2 (2008): 72-82 describes a technique known as Compressed Sesnsing (CS) where Magnetic Resonance (MR) images are acquired using sparse sampling of k-space.